The Mole and the Avogadro Constant

Key definitions

• The mole, mol, is the unit of amount of substance and that one mole contains $6.02\times 10^{23}$ particles, (e.g. atoms, ions, molecules). This is the Avogadro’s constant.
• The molar mass of a substance is the mass of 1 mole of its particles.

Main formula

$$\text{amount of substance (mol)}=\frac{\text{mass (g)}}{\text{molar mass (g / mol)}}$$

• Using this relationship, you are able to calculate:
  • the amount of substance (mol)
  • mass
  • molar mass ${\text{M}}_{\text{r}}$
  • relative atomic mass ${\text{A}}_{\text{r}}$ or relative molecular/formula mass ${\text{M}}_{\text{r}}$
  • number of particles, using the value of Avogadro’s constant.

Finding the molar mass

• The molar mass of a substance is the mass of 1 mole of its particles.

1. Write down the symbol or formula of the substance.
2. Find its ${\text{A}}_r$ or ${\text{M}}_r$.
3. Express that mass in grams (g).

Reactions involving gases

• The molar gas volume is taken as $24{\text{dm}}^3$ at room temperature and pressure, r.t.p., in calculations involving gases.

Formula for calculating the number of moles

$$\text{no. of moles}=\frac{\text{vol at r.t.p.}}{24{\text{dm}}^3}$$

• Using this relationship, you are able to calculate:
  • the number of moles
  • the volume at room temperature and pressure, r.t.p.

The concentration of a solution

• The concentration of a solution is the amount of solute that is dissolved in $1{\text{dm}}^3$ of solution. This can be expressed in grams, or moles.
• Remember that:
  • the solute is the substance you dissolve in a liquid to make a solution
  • the solvent is the liquid you use (usually water).

Formula for calculating the concentration of a solution

$${\text{conc (mol/dm}}^3{\text{ or g/dm}}^3\text{)}=\frac{\text{amount (mol)}}{{\text{volume (dm}}^3\text{)}}$$

• Using this relationship, you are able to calculate:
  • the concentration of a solution
  • the amount of solute present
  • the volume

Finding the concentration in moles

• This is how to find the concentration of a solution in moles per ${\text{dm}}^3$.

1. Find the ${\text{M}}_r$ of the solute.
2. Use the equation above to calculate the concentration of a solution.

Finding the empirical formula

• The empirical formula shows the simplest ratio in which atoms combine to form a compound.

1. Find the masses that combine (in grams) by experiment.
2. Change grams to moles of atoms.
3. You are able to find the ratio in which atoms combine.
4. With the ratio, you can write the formula.

Template

Finding % yield and % purity

• The yield is the amount of product you obtain from a reaction.
• To have something pure means that only one substance is in it. You might need to minimize the amount of impurities.

Finding the % yield

$$\text{\% yield}=\frac{\text{actual mass of product obtained}}{\text{theoretical mass of product}}\times 100\%$$

Finding the % purity

$$\text{\% purity of a product}=\frac{\text{mass of the pure product}}{\text{mass of the impure product obtained}}\times 100\%$$